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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.24026 |
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| _version_ | 1866911030006775808 |
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| author | Wang, Yongyi Li, Wenxin |
| author_facet | Wang, Yongyi Li, Wenxin |
| contents | In the domain of algorithmic decision-making, non-Markovian dynamics manifest as a significant impediment, especially for paradigms such as Reinforcement Learning (RL), thereby exerting far-reaching consequences on the advancement and effectiveness of the associated systems. Nevertheless, the existing benchmarks are deficient in comprehensively assessing the capacity of decision algorithms to handle non-Markovian dynamics. To address this deficiency, we have devised a generalized methodology grounded in category theory. Notably, we established the category of Markov Decision Processes (MDP) and the category of non-Markovian Decision Processes (NMDP), and proved the equivalence relationship between them. This theoretical foundation provides a novel perspective for understanding and addressing non-Markovian dynamics. We further introduced non-Markovianity into decision-making problem settings via the History Aggregator for State (HAS). With HAS, we can precisely control the state dependency structure of decision-making problems in the time series. Our analysis demonstrates the effectiveness of our method in representing a broad range of non-Markovian dynamics. This approach facilitates a more rigorous and flexible evaluation of decision algorithms by testing them in problem settings where non-Markovian dynamics are explicitly constructed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_24026 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Constructing Non-Markovian Decision Process via History Aggregator Wang, Yongyi Li, Wenxin Artificial Intelligence In the domain of algorithmic decision-making, non-Markovian dynamics manifest as a significant impediment, especially for paradigms such as Reinforcement Learning (RL), thereby exerting far-reaching consequences on the advancement and effectiveness of the associated systems. Nevertheless, the existing benchmarks are deficient in comprehensively assessing the capacity of decision algorithms to handle non-Markovian dynamics. To address this deficiency, we have devised a generalized methodology grounded in category theory. Notably, we established the category of Markov Decision Processes (MDP) and the category of non-Markovian Decision Processes (NMDP), and proved the equivalence relationship between them. This theoretical foundation provides a novel perspective for understanding and addressing non-Markovian dynamics. We further introduced non-Markovianity into decision-making problem settings via the History Aggregator for State (HAS). With HAS, we can precisely control the state dependency structure of decision-making problems in the time series. Our analysis demonstrates the effectiveness of our method in representing a broad range of non-Markovian dynamics. This approach facilitates a more rigorous and flexible evaluation of decision algorithms by testing them in problem settings where non-Markovian dynamics are explicitly constructed. |
| title | Constructing Non-Markovian Decision Process via History Aggregator |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2506.24026 |